Without looking at any numbers, halving may not be the way to go. The reason is that the strength of a piece of wood is not in a direct mathematical relationship to its size, rather it is a functional relationship. In other words, a 4x4 is not half the strength of an 8x8 (consider the fact that a 4x4 square has 1/4, not 1/2, or the area of an 8x8 square) And as you said, 1 1/2 inch braces are kind of silly. I might be wrong (as I said, I haven't mathematically figured it out, just goin off of intuition) but I would think you would want something in the range of 2/3 to 3/4 of the original timber size, not half.